Measuring the Span of the Visible Universe with Nonparametric Regression

• Activity Number: 470
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Irina Udaltsova*+ and Samuel Schmidt and Jiming Jiang
• Companies: University of California at Davis and University of California at Davis and University of California at Davis
• Keywords: astrostatisics ; nonparametric ; kernel regression

Abstract

This talk presents an adaptive kernel regression technique for estimation in multiple dimensions. We apply the method to determine galaxy redshifts using photometry. The kernel regression is a nonparametric procedure for estimation of response variable based on locally weighted average of neighboring data points. The weights assume a distance-based kernel function with a pre-defined distance metric. Parallel to image processing and reconstruction ideas, a desirable property of the estimator is the recovery and noise removal of image. It seems appropriate that local image features should guide the estimation procedure. Orientation features in an image are summarized into image gradients, which re-define the distance metric according to the local dominant orientation. Adapted size and shape of the regression kernel give appropriate influence to local data points, resulting in preservation of image details. Such technique is proposed for use in multiple dimensions. Simulation and application to photometric data are also presented.